
/*
 * -- SuperLU routine (version 2.0) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * November 15, 1997
 *
 */
/*
 * File name:	zlaqgs.c
 * History:     Modified from LAPACK routine ZLAQGE
 */
#include <math.h>
#include "slu_zdefs.h"

void
zlaqgs(SuperMatrix *A, double *r, double *c,
       double rowcnd, double colcnd, double amax, char *equed)
{
    /*
        Purpose
        =======

        ZLAQGS equilibrates a general sparse M by N matrix A using the row and
        scaling factors in the vectors R and C.

        See supermatrix.h for the definition of 'SuperMatrix' structure.

        Arguments
        =========

        A       (input/output) SuperMatrix*
                On exit, the equilibrated matrix.  See EQUED for the form of
                the equilibrated matrix. The type of A can be:
    	    Stype = NC; Dtype = SLU_Z; Mtype = GE.

        R       (input) double*, dimension (A->nrow)
                The row scale factors for A.

        C       (input) double*, dimension (A->ncol)
                The column scale factors for A.

        ROWCND  (input) double
                Ratio of the smallest R(i) to the largest R(i).

        COLCND  (input) double
                Ratio of the smallest C(i) to the largest C(i).

        AMAX    (input) double
                Absolute value of largest matrix entry.

        EQUED   (output) char*
                Specifies the form of equilibration that was done.
                = 'N':  No equilibration
                = 'R':  Row equilibration, i.e., A has been premultiplied by
                        diag(R).
                = 'C':  Column equilibration, i.e., A has been postmultiplied
                        by diag(C).
                = 'B':  Both row and column equilibration, i.e., A has been
                        replaced by diag(R) * A * diag(C).

        Internal Parameters
        ===================

        THRESH is a threshold value used to decide if row or column scaling
        should be done based on the ratio of the row or column scaling
        factors.  If ROWCND < THRESH, row scaling is done, and if
        COLCND < THRESH, column scaling is done.

        LARGE and SMALL are threshold values used to decide if row scaling
        should be done based on the absolute size of the largest matrix
        element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.

        =====================================================================
    */

#define THRESH    (0.1)

    /* Local variables */
    NCformat *Astore;
    doublecomplex   *Aval;
    int i, j, irow;
    double large, small, cj;
    extern double dlamch_(char *);
    double temp;


    /* Quick return if possible */
    if (A->nrow <= 0 || A->ncol <= 0) {
        *(unsigned char *)equed = 'N';
        return;
    }

    Astore = A->Store;
    Aval = Astore->nzval;

    /* Initialize LARGE and SMALL. */
    small = dlamch_("Safe minimum") / dlamch_("Precision");
    large = 1. / small;

    if (rowcnd >= THRESH && amax >= small && amax <= large) {
        if (colcnd >= THRESH)
            *(unsigned char *)equed = 'N';
        else {
            /* Column scaling */
            for (j = 0; j < A->ncol; ++j) {
                cj = c[j];
                for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
                    zd_mult(&Aval[i], &Aval[i], cj);
                }
            }
            *(unsigned char *)equed = 'C';
        }
    } else if (colcnd >= THRESH) {
        /* Row scaling, no column scaling */
        for (j = 0; j < A->ncol; ++j)
            for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
                irow = Astore->rowind[i];
                zd_mult(&Aval[i], &Aval[i], r[irow]);
            }
        *(unsigned char *)equed = 'R';
    } else {
        /* Row and column scaling */
        for (j = 0; j < A->ncol; ++j) {
            cj = c[j];
            for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
                irow = Astore->rowind[i];
                temp = cj * r[irow];
                zd_mult(&Aval[i], &Aval[i], temp);
            }
        }
        *(unsigned char *)equed = 'B';
    }

    return;

} /* zlaqgs */

